Below is the question I put up when we first started the Trig section. It was the teaser. I put them into groups of 4 and had them come up with questions, statements, whatever.
I think I originally saw a picture like this on Yummy Math or some variation thereof. In the spirit of making the problem more rich (and because Hubby and I heat with wood that we take from our property...often in situations just like the picture!), I chose to ask how many logs I could get from the tree.
Most saw the right triangle right away, and many wanted to use Pythagoras (aka The Greek Geek) to find out how long the main part of the tree was. They were told that it was too dangerous to get up on the trunk and actually measure it, the tree it is hung up in is too skinny too climb. They had some more thoughts and then asked the question: "If we don't have 2 sides, how can we do this??" Huzzah! And off we went into discovering (all over again) about trig ratios.
SO, when I was trying to figure out what to do for an assessment, I realized: OH! We never answered the teaser question! I paired them up (thus taking care of the one with the concussion), put this pic back up on the board, and pointed out that the angle of elevation was 40 degrees and that Hubby and I measured out 100 ft on the ground. Then I gave them one more question that related to our Precision Machine Shop and gave them these instructions:
- You and your partner must answer these 2 questions together. Be sure I can see your work.
- You may ask each other questions, make observations, etc, but not a single word can be spoken aloud. Everything you want to ask or point out has to be on paper. (Yeah, this is not original either. Love all of you bloggers: I saw someone had done this on the larger whiteboards, but I only have 5 of the larger whiteboards, so I had to resort to pink paper ....Breast Cancer Awareness Day at school).
I was blown away. For all the times I have let my students do partner quizzes, I would wander and listen, but never had a record of their thought processes. I was AMAZED at how many of my 23 students would have bombed this quiz because of their inattentiveness to units of measure. Only one grouping (the only trio!) made an error. Not one of the three thought there was anything wrong with an answer of: "Seven 18 inch logs can be gotten from this tree." This in spite of the fact that the picture they had in front of them to work from had 100 ft clearly labeled on the ground. Yowch!
Needless to say, I have to figure out a way to incorporate more dimensional analysis!